Helical post-buckling of a rod in a cylinder: with
applications to drill-strings
J.M.T. Thompson, M. Silveira, G.H.M. van der Heijden &
M. Wiercigroch
The helical buckling and post-buckling of an elastic rod within a cylindrical
casing arises in many disciplines, but is particularly important in the
petroleum industry. Here a drill-string, subjected to an end twisting moment
combined with axial tension or compression, is particularly prone to buckling
within its bore-hole: with potentially serious results. In this paper we make
a detailed theoretical study of this type of instability, deriving precise
new results for the advanced post-buckling stage when the rod is in continuous
contact with the cylinder. Results, including rigorous stability analyses and
contact pressure assessments, are presented as equilibrium surfaces to
facilitate comparisons with experimental results. Two approximate solutions
give insight, universal graphs and parameters, for the practically-relevant
case of small angles, and highlight the existence of a critical cylinder
diameter. Excellent agreement with experiments is achieved.
keywords: rod mechanics, drill-strings, post-buckling, helical buckling
Proc. R. Soc. Lond. A 468, 1591-1614 (2012)